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This paper studies the distributed adaptiveestimation problems for stochastic large regression modelswith an infinite number of parameters. By constructing a re-cursive local cost function, we propose a novel distributedrecursive least…

We describe stochastic Newton and stochastic quasi-Newton approaches to efficiently solve large linear least-squares problems where the very large data sets present a significant computational burden (e.g., the size may exceed computer…

We consider multistage stochastic linear optimization problems combining joint dynamic probabilistic constraints with hard constraints. We develop a method for projecting decision rules onto hard constraints of wait-and-see type. We…

In this paper, we present a sparse grid-based Monte Carlo method for solving high-dimensional semi-linear nonlocal diffusion equations with volume constraints. The nonlocal model is governed by a class of semi-linear partial…

Radial basis functions have become a popular tool for approximation and solution of partial differential equations (PDEs). The recently proposed multilevel sparse interpolation with kernels (MuSIK) algorithm proposed in \cite{Georgoulis}…

This paper provides a non-asymptotic analysis of linear stochastic approximation (LSA) algorithms with fixed stepsize. This family of methods arises in many machine learning tasks and is used to obtain approximate solutions of a linear…

Variable selection and dimension reduction are two commonly adopted approaches for high-dimensional data analysis, but have traditionally been treated separately. Here we propose an integrated approach, called sparse gradient learning…

The Linearized Laplace Approximation (LLA) has been recently used to perform uncertainty estimation on the predictions of pre-trained deep neural networks (DNNs). However, its widespread application is hindered by significant computational…

The generalized linear model (GLM) plays a key role in regression analyses. In high-dimensional data, the sparse GLM has been used but it is not robust against outliers. Recently, the robust methods have been proposed for the specific…

There is an increasing need in solving high-dimensional optimization problems under non-deterministic environment. The simultaneous perturbation stochastic approximation (SPSA) algorithm has recently attracted considerable attention for…

We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…

Penalized logistic regression is extremely useful for binary classification with large number of covariates (higher than the sample size), having several real life applications, including genomic disease classification. However, the…

In recent years, network models have gained prominence for their ability to capture complex associations. In statistical omics, networks can be used to model and study the functional relationships between genes, proteins, and other types of…

The one-dimensional pseudo Leja sequences introduced in \cite{bialas2012pseudo}, as an alternative to Leja sequences, provides us with good interpolation nodes for the approximation of holomorphic functions. We propose a definition of…

We propose new methods for multivariate linear regression when the regression coefficient matrix is sparse and the error covariance matrix is dense. We assume that the error covariance matrix has equicorrelation across the response…

Stochastic collocation methods for approximating the solution of partial differential equations with random input data (e.g., coefficients and forcing terms) suffer from the curse of dimensionality whereby increases in the stochastic…

Although there is much recent work developing flexible variational methods for Bayesian computation, Gaussian approximations with structured covariance matrices are often preferred computationally in high-dimensional settings. This paper…

Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…

Nowadays an increasing amount of data is available and we have to deal with models in high dimension (number of covariates much larger than the sample size). Under sparsity assumption it is reasonable to hope that we can make a good…

This paper introduces a new methodology to analyse bipartite and unipartite networks with nonnegative edge values. The proposed approach combines and adapts a number of ideas from the literature on latent variable network models. The…